Abstract: It seems empirically that the first digits of random numbers do not occur with equal frequency. After making many counts from a large body of physical data, such as the Farmer's Almanac, census reports, etc., F. Benford first noticed that the proportion of numbers with first significant digits equal to or less than k (k=1,2, ... , 9) is approximately log10(k+1). Hence this logarithmic law for the first significant digits is called Benford's law. In this paper we show another example of this type and also give a Benford sequence in the sense of natural density which is not a strong Benford sequence.